Korean War 
On the one hand a conflict between North and South Korea; on the other an example of Proxy Wars between the [United States] and the Soviet Union. It started on June 25th (Korean time), 1950 when North Korean troops crossed the 38th parallel, invading South Korea.
But first some backstory:
When World War II came to an end in 1945, there emerged the problem of what to do with the surrender of Japanese troops in the Korean peninsula, which up to that point had been one unified country. Since the Soviet troops were fighting the Japanese in the north, the U.S. proposed the idea of splitting the peninsula in half at the 38th parallel; the U.S. would deal with the Japanese troops in the south and the Soviets the north. The Soviet Union was surprisingly agreeable in this arrangement.
The plan was for this setup to be temporary until the United Nations could hold an election in the peninsula to establish autonomy for Korea. And they did elect Syngman Rhee in 1948, but the Soviet Union apparently had other plans. Instead of allowing the people to participate in the election they installed communist sympathizer Kim Il-sung as prime minister of the North, now the “Democratic People’s Republic of Korea.” (Talk about [propaganda].)
So it didn’t look like Korea was going to be reunified anytime soon, and the U.S. didn’t seem particularly eager to make it a long-term effort. They withdrew troops from the South in 1949 while in the North the Soviets were equipping and training a substantial army. Hmmm.
But still it came as a surprise, at least to the U.S., when North Korea invaded the South in 1950. It’s debatable how much of the Soviet Union’s idea it was, but even if Kim Il-sung was the mastermind, the Soviets were happy to contribute to the cause in the form of supplies. And anyway, at the time the U.S. was beginning to consider the Soviet Union an Evil Empire and was ready to assume the worst about them. Once [President Harry Truman] heard of the invasion he authorized the use of force to defend the South and General Douglas Mac Arthur to take command of a counterattack. The U.N. voted to assist the cause and several other countries sent troops.

The retaliation was successful, particularly at the [Inchon Landing], and the entire peninsula was retaken by October of 1950. However, China was very wary of U.S. presence so close and warned that if any troops crossed the North Korean border, the U.S. would be sorry. Truman concurred. MacArthur apparently didn’t care, though, and perhaps either because he was a [megalomaniac] or for [someother] reason, tried to go on invading China and who knows what else.

Consequently, the Chinese entered the war on October 19, 1950 and initiated the longest-ever retreat of the U.S. army. At that point MacArthur would have liked to have nuked the Chinese just a little bit, but instead was fired by Truman in early 1951. [General Matthew Ridgway] took over.

Not much else happened the rest of the war except smaller-scale fighting around the 38th parallel, which is where the two sides established rough equilibrium, but it lasted until August 1953 when a truce was agreed upon. Even today a peace treaty has not yet been signed, and the border between North and South remains the most heavily guarded in the world.
 The border between North and South Korea at Panmunjeom.
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